We report a new approach to obtaining single-transverse-mode operation of a multimode fiber amplifier in which the gain fiber is coiled to induce significant bend loss for all but the lowest-order mode. We demonstrated this method by constructing a coiled amplifier using Yb-doped, double-clad fiber with a core diameter of 25 microm and a numerical aperture of ~0.1 (V approximately 7.4) . When the amplifier was operated as an amplified-spontaneous-emission source, the output beam had an M(2) value of 1.09 +/- 0.09 ; when seeded at 1064 nm, the slope efficiency was similar to that of an uncoiled amplifier. This technique will permit scaling of pulsed fiber lasers and amplifiers to significantly higher pulse energies and peak powers and cw fiber sources to higher average powers while maintaining excellent beam quality.